Alphabet$($GOOGL$)$ has yet to pay a$$ dividend, but in spring $2018$ it announced it would repurchase $$8\mathrm{.}5$ billion worth of shares over the year.$($Actually$,$ the exact amount was $$8,589,869,056$known as a$$ "perfect" number because it is equal to the sum of its$$ divisors$).$ If the amount spent on share repurchases were expected to grow by $6\mathrm{.}6\%$ per$$ year, and$$ Alphabet's equity cost of capital is $8\%,$ estimate$$ Alphabet's market capitalization. If Alphabet has $691$ million shares$$ outstanding, what stock price does this correspond$$ to$?$

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Part $1$

The share price is $$$